The Nginx cache directories descend from /var/cache/nginx and are named by the domain domains. To empty an Nginx cache, you can simply delete the corresponding cache directory from that tree.
In your screenshot you are referring to a temporary directory where Nginx downloads files that it shall cache, then moves these files into their real cache directories. Normally, /var/lib/nginx/nginx/proxy/* should be almost empty at all times. If it is not, maybe a website or your Nginx server has a wrong configuration, e.g. the "proxy_cache_path" set to a wrong value or maybe even to /var/lib/proxy instead of their final destination. If you have installed Nginx through Plesk and let Plesk configure it for your, it should all be configured correctly. If you have added your own configurations or not had Nginx installed through Plesk or modified it later, that could lead to the issue described above.
You could try to run
# grep -R proxy_cache_path /etc/nginx/*.* | grep /var/lib/proxy
to identify entries for that the proxy_cache_path line includes a reference to /var/lib/proxy. As far as I know, it is safe to remove the proxy/* directories as they should be recreated when Nginx needs them.